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Unique Audiance For A Fairy Tale

A sultan has 14 daughters. He decides to tell every night four of his daughters a fairy tale, but in such a way that every night, there will be another combination of four daughters. How many nights will keep the sultan busy telling fairy tales? 

Finding Unique Audiance For A Fairy Tale - Maths Puzzle

Find number of nights here!

Nights For Fairy Tales!


Story behind the title?

For a moment, let's name all the daughters as A, B, C, D, E.....N. 

There are 14 x 13 x 12 x 11 = 24024 combinations of daughters. But in these combinations, lots of combinations are repeated. For example, ABCD combination is same as ABDC or DABC etc. There can be 4 x 3 x 2 x 1 = 24 combinations while considering group of 4 daughters here for example it is A, B, C, D. For these 24 combination we should count only 1 as a unique combination.

Hence for 24024 combinations, we have 24024/24 = 1001 unique combination. 

Busy Nights For Fairy Tales! - Maths Puzzle


In short, Sultan would be busy for 1001 nights in telling fairy tales to his 14 daughters in unique combinations.
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